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Before attempting to go into the ants' nest, you should first save
Elmer to get more flamethrower fuel.  Some time between the 8th and
10th (I don't remember the exact day), he will leave a note in his
station saying that he is going hiking in the SW volcanic cone.  Go to
the volcano, fight the ants, and next day, visit Elmer's station.
He'll thank you for saving his life and give you more flamethrower
fuel.  The entrance to the ants' nest will never appear on the main
map, but there are several other ways to get there:

 - By taking a flight from Hilber's field.
 - By driving a tank from a battle going on at a nearby location.
 - By going south when you are in a battle at the M1 mine.

The entrance to the nest doesn't stay open long enough for you to get
in before the ants start invading the various locations in the town,
so you'll have to wait until they do.  The 11th is the best day to
enter the hole since it is very hot and there are few ants around.  If
you try cooler days, there will probably be too many of them around
for you to handle.  Also, if you decide to get to the hole by plane,
you can land safely on the dirt road parallel to the tracks leading to
the m1 mine.

For those who are having trouble getting to the ants hideout, it is
located about one screen due south of mine one.  The best way to gain
access to the tunnel is on the morning of day 11.  Go to the airport
and get the plane.  Fly to mine one (southeast from the airport) and
land on the road in front of mine one.  Get out of your plane and walk
to the center of the main building of mine one.  Walk south about one
and a half screens and the hole should open and a ant will crawl out.
You must kill the ant and run to the hole before it closes.  You will
get about 4 or 5 chances to get in.  Once you are in the hole you will
automatically have the flame thrower and the timed dynamite charges.
There are two levels of the ants chambers, a top level and a bottom
level.  You must make a map as to where you have checked.  You can do
this by putting the game on pause with the left mouse button.  This
will keep the ants off you while you draw maps.  Once you have made it
to the bottom chamber repeat the map drawing until you find the Queen
ant's chamber.  You will need it to get out after you plant the
charges.  To plant the charges once in the Queen's chambers, move
close to the queens left side of her body.  Once you walk around her
left side the music will stop and a slow ticking will start.  You will
have to get back to the place you entered on the second level.  If you
get back before the bomb goes off you will win the game.

NOTE:

You need all the four pieces of evidence to convince the Mayor.  The
four pieces of evidence are:

 - Ant tracks (volcano or the farm at the bottom right)
 - Fluid sample (Neptune Hall or quarry)
 - Body part of an ant (just shoot the antennas of one ant at Mine 1,
   volcano, a farm or anywhere else)
 - A recording of an ant (you can get it at the police station or make
   a recording yourself by using a plane).

You also have to send the rock samples at the beginning to the
government lab, so you can prove to the Mayor that Dr. Wells can be
trusted.

You can save important time by escaping the hospital.

Even with the solution given above you still must learn how to fly the
airplane.  To get the right altitude to save fuel, take off and then
fly east or west.  Back off the throttle until the shadow on the
ground comes up and just touches the wing of the plane.  You will then
have the right speed and altitude.  The faster you fly and the higher
you go, the more fuel you will use.  These settings will conserve
enough fuel to let you fly and not run out of gas and return to the
airfield and land if you blow it getting into the ant hole.